Method for detecting geometrical-optical abberations

ABSTRACT

The invention relates to a method for determining geometrical-optical aberrations up to and including  3 rd order in particle-optical, probe-forming systems, in particular scanning electron microscopes, comprising an essentially punctiform source, lenses, an object, and a detector, the image being recorded ( 6 ), the process being repeated with an overfocussed and an overfocussed beam, the images ( 6, 6   a,    6   b ) being transformed in Fourier space, the transformation of the overfocussed image ( 7   a ) and the underfocussed image being divided ( 8 ) by that of the transformed focussed image ( 7 ), and the result being reverse transformed, and the brightness profiles of the probes ( 5, 5   a ), that is to say the images of the source ( 1 ) being determined in overfocus and underfocus, the asymmetry, the width and/or the curvature of the profile ( 9, 9   a ) being determined in the center, and the image aberration being determined from the differences.

[0001] The invention relates to a method for determining geometrical-optical aberrations up to and including 3rd order in particle-optical, probe-forming systems, in particular scanning electron microscopes comprising an essentially punctiform source, which emits the particles, lenses for influencing the particle beam, an object, which is imaged by the particles, and a detector for registering the particles or imaging the object, the object being imaged by means of a particle beam focussed on the object, and the image being recorded, the process being repeated with an overfocussed and an overfocussed beam, which produce the images (overfocussed) and (underfocussed), the images being transformed in Fourier space, the transformation of the overfocussed image being divided by that of the transformed focussed image, and the quotient being obtained, and the transformation of the underfocussed image being divided by that of the transformed focussed image and the quotient being obtained.

[0002] Scanning electron microscopes operate according to the principle that a sharply focussed electron beam, whose diameter determines the efficiency and resolution, is guided line by line over an object surface to be analysed. The electrons passing through the object or scattered back therefrom, or the secondary electrons released in the object surface, are either collected in a collector or amplified by means of a scintillator and a downstream photomultiplier and used for controlling the display. For emission of the electrons, a source under high voltage is used, which usually takes the form of a tungsten tip, whose diameter is of the order of a few nm. By means of said tip, an essentially punctiform particle source can be provided with virtually any accuracy. The image of the source, that is to say the tungsten tip, by means of the microscope optics is usually described as the probe.

[0003] In the case of particle optical systems, in particular scanning electron microscopes, the resolution capacity and the quality of the image is limited, inter alia, by the geometrical-optical aberrations, which have the consequence that punctiform objects are not reproduced in an ideally punctiform manner in the image. In the vicinity of the theoretical image point, the caustic is produced as the envelope of the rays actually intersecting in its vicinity. Spherical aberration is known, in which the axially parallel incident rays intersect in the image space respectively before or after the image point supplied by the paraxial rays. The axial image aberrations of higher “foldedness” lead to enlargements of the image point, which will be different depending on the azimuth. In the case of two-fold astigmatism, a circular object in the image plane is distorted into an elliptical image, since the meriodonal and sagittal rays perpendicular thereto have different focal lengths. For correction of these axial imaging aberrations extending up to 3rd order, it is known to use correctives consisting of non-circular lens systems, as well as, for example from PCT/DE98/02596, a method for eliminating all axial image aberrations up to 3rd order in order to increase the resolution capacity.

[0004] The article in Japanese Journal Appl. Phys., Volume 38 (1999), pages 957ff, and GB 2 305 324 A disclose methods for determining 1st order image aberrations, in which the images from two different focussings are transformed in Fourier space and, by forming the quotient, are used for determining the image aberration coefficients. The method described here is unsuitable for determining higher order image aberrations.

[0005] A disadvantage of this can be seen in the fact that the information obtained in the image point is determined both by the optical image aberrations of the imaging, probe-forming optical system and by the object structure itself. For determination of the image aberration, it would therefore be necessary to know the object structure, in order, from the image obtained, and the known object structure to be able to draw conclusions about the nature and size of the image aberration.

[0006] On the basis of the prior art, the object of the invention is to provide a method, with which the geometrical-optical imaging aberration can be determined, without an exact knowledge of the object structure, which is imaged by the particle beam emitted by the source.

[0007] According to this invention, this object is achieved in that both quotients are reverse transformed and thereby the brightness profiles of the probes, that is to say of the images of the source in overfocus and underfocus, are determined, the asymmetry (AS) of the profiles with respect to the center, the width (BR) of the profiles, in particular the half-value width, and/or the curvature (KR) of the profiles in the centre is determined, and the differences of the profiles of the probes with respect to these parameters are used to determine the image aberrations.

[0008] The basic finding of the invention consists in the fact that, on transformation of the images of the object with a particle beam focussed on the object and an overfocussed and an underfocussed particle beam, and by subsequent division of the transforms in Fourier space, the object structure is cancelled out of the quotients obtained. The image corresponds mathematically to a folding of the object with a focussed or defocussed probe, that is to say in Fourier space to a product of object information and probe information. Consequently, after the Fourier transformation, the object information can be cancelled out by a division of the two transforms. That means that, by division in Fourier space, the information, contained in the transformations of the images, about the object to be imaged can be eliminated, so that the information about the optical image aberrations remains. By this means, in conventional terminology, the terms underfocussed and overfocussed mean that the particle beam is not focussed in the object plane, but before or after it with respect to the optical axis. If the defocus is large with respect to the probe diameter, with an image with a focussed particle beam, the focussed image is an approximately adequate reproduction of the object structure. The condition necessary for this, of an essentially punctiform source, is sufficiently satisfied by the above-described tungsten tip. In this case the defocussed probe, that is to say an image of the source with a defocussed particle beam, can be obtained from the reverse transformation of the quotient, which no longer contains information about the object structure. After this reverse transformation, the geometrical-optical image aberrations are determined, which lead to the distortion of the probe profiles. To this end, sections are formed through the probe profiles to determine the profiles of intensity, or brightness, of the images in the profile, that is to say perpendicular to the optical axis. The sections are, as discussed below, formed at equidistant angular intervals, in order also to determine the brightness and intensity distribution of the image about the optical axis. To determine the geometrical-optical image aberrations, the asymmetry of the profiles with respect to the center are determined by subtracting the measurement values of the sections to the left and right of the center from one another, the width of the section, the half-value width and/or its curvature in the center usually being chosen here to simplify the evaluation. From these values, which are usually different, for the overfocussed and underfocussed probes, mean values and/or differences can also be formed. These angle-dependent values can be used by the person skilled in the art to determine the image aberrations, and from the latter, by setting a corrective or by means of mathematical image reconstruction methods, the correction can be made to obtain a sharp, undistorted image.

[0009] The advantage of the invention consists in the fact that only one object needs to be imaged multiply in order, from the focussed, overfocussed and underfocussed images, to determine the geometrical-imaging aberration without the actual structure of the object needing to be known. From this, correction parameters can be determined, with which, with subsequent measurement series and different objects, the obtained measurement results, i.e. images, can be corrected to obtain a sharp image. To this end the optics of the system are analogously adjusted by appropriately setting a corrective, or mathematical correction methods are applied to compensate for the aberrations.

[0010] Advantageous embodiments of the method are the subject of sub-claims.

[0011] For carrying out the Fourier transformation in the case of a particle beam focussed or defocussed on the object, it is proposed that the transformation be carried out mathematically, in particular according to the fast-Fourier transformation known to the person skilled in the art. In principle, it is also possible to carry out such a transformation in an analogous manner by producing a diffraction pattern. With the same method, reverse transformations of the respective quotients can also be carried out.

[0012] In particular in the case of scanning electron microscopes, the lenses for influencing the direction of the electron beam consist of electrical and/or magnetic multipoles, since these can focus and deflect the electron beam in a manner known to the person skilled in the art. With these types of lenses, a correction of the geometrical-optical imaging aberration can also be provided in a simple manner, since a correction factor determined by the method described above can be applied to the electrical and/or magnetic fields, that is to say they can be varied, to obtain an aberration-free image of the object.

[0013] To ensure that the information about the object structure is actually cancelled out by division in Fourier space, the width of the focussed probe, that is to say the image of the source in the defocussed state, must be at least ten times greater than the width of the focussed probe, or the actual width of the particle source.

[0014] Advantageously, the sections through the probe profiles are placed at equidistant angular intervals, in particular every 15 degrees, to obtain adequate resolution of the brightness or intensity profiles about the optical axis. To determine the geometrically optical imaging aberrations, the “foldednesses” of the sections are analysed, that is to say how many planes of symmetry the probe profile has perpendicular to the optical axis.

[0015] The asymmetry of the sections serve for determining the second order image aberration. Since these ought to be theoretically the same in overfocus and underfocus, the mean value can be formed from the two measurements for further analysis, this mean value formed from overfocus and underfocus and dependent on the section angle w, being subjected to analysis, with respect to the section angle, of the one-fold and three-fold angle components, for example by means of a Fourier analysis, according to the section angle w. The one-fold component, as regards the orientation and magnitude, represents the value of the 2nd order axial coma; the three-fold component of the analysis supplies, as regards orientation and magnitude, the value of the three-fold 2nd order astigmatism.

[0016] The widths BR (w) and curvatures KW (w) of the probe profiles, which are dependent on the section angle w, can be used for the determination of further geometrical-optical image aberrations. In general terms, the width BR of the probe profiles provides a basis for determining the 1st order image aberration, and the determined values of curvature KR for determining the values of the 3rd order image aberration. For analysis, however, the following procedure is necessary: the common feature is that the differences between the measured values for overfocus and underfocus are determined in dependence on the section angle w. In the aberration-free case, the differences would disappear. Here, too, an analysis of the obtained difference values according to their foldedness with respect to the section angle w should be carried out, for example by means of Fourier analysis. In this way, the spectrum components, ordered according to their foldedness, are obtained in dependence on the section angle w. The corresponding foldedness permits the assignment to the corresponding geometrical-optical image aberrations, the quantitative value and—apart from the rotationally symmetrical image aberrations—its orientation provide information about the magnitude and, possibly, the alignment of a particular image aberration. In principle, the widths BR of the probe profiles and/or the differences in overfocus/underfocus allow determination of the 1st order image aberrations, namely defocussing and 1st order two-fold astigmatism. The zero-fold component determined via the section angle of the difference of the width, that is to say the mean value formed via the section angle w, which is therefore direction independent, provides a dimension figure for the focussing and defocussing of the electron-optical system. The first order zero-fold image aberration represents the defocussing.

[0017] The two-fold component, determined by the same Fourier analysis, from the difference of the widths of the probe profiles, provides, according to magnitude and orientation, the value of the aberration of the 1st order two-fold astigmatism.

[0018] From the curvatures of the probe profiles KR (w) and the differences formed from overfocus and underfocus, the individual aberration components of the 3rd order image aberrations can also be obtained by an analysis of the foldedness via the section angle, carried out, for example, by means of Fourier analysis. Here, too, particular image aberrations are assigned in dependence on the foldedness, the size of the component giving the magnitude and orientation of the image aberration present. For example, the zero-fold component, that is to say the mean value of the section angle w, indicates a dimension figure for the 3rd order spherical aberration. The two-fold component, according to its magnitude and direction, gives the dimension figure for the 3rd order stellar aberration. Finally, the four-fold component, also according to its magnitude and direction, gives the value for the four-fold astigmatism. Thus all 3rd-order electron-optical image aberrations are determined.

[0019] Since in real optical systems the 1st and 3rd order image aberrations are never completely decoupled in width and curvature, a more accurate determination of 3rd order aberrations can be carried out using, instead of the curvature (KR) or width (BR) or their respective differences, linear combinations of the two values according to the aforementioned scheme. The respective associated multiplication factors α and β according to the formula:

α*BR+β*KR

[0020] must be determined empirically for each particle-optical system to obtain the best possible results. For the 3rd order spherical aberrations, the mean value over the section angle w must be formed.

[0021] Further details, features and advantages of the invention can be taken from the following descriptive part, wherein exemplary embodiments of the invention are described in greater detail with reference to a plurality of drawings, in which

[0022]FIG. 1 shows a schematic view of a scanning electron microscope,

[0023]FIG. 2 shows a flow diagram for determining the probe form,

[0024]FIG. 3 shows an analysis of a probe profile, and

[0025]FIGS. 4 and 5 show sections through a probe profile

[0026] The exemplary embodiment of the invention shown in FIG. 1 is a scanning electron microscope, in which electrons are emitted from a source (1), usually an approximately punctiform tungsten tip, and are guided by means of lenses (2), such as electrical and/or magnetic multipoles, line by line over the object (3) to be imaged, as indicated by the arrows. The electrons radiated back by the object (3), or the secondary electrons emitted from it, are registered by means of a suitable detector (4), which registers an image in the form of a brightness or intensity distribution.

[0027]FIG. 2 shows the procedure by means of which the probe forms (5, 5 a) are obtained. To this end, the object (3) is imaged with a focussed, an overfocussed and an underfocussed particle beam, and subsequently these images (6, 6 a, 6 b) are subjected to a Fourier tranformation. After division (8) of the transform (7 a) of the overfocussed image by the transform (7) of the focussed image, and the reverse transformation of the quotient, the information about the imaged object (3), which was still contained in the original images (6, 6 a, 6 b), is cancelled out, and, as a result, only the form of the probe in overfocus and underfocus (5, 5 a) is obtained. The same procedure is carried out for the (7 b) transform in underfocus.

[0028] Subsequently, as shown in FIG. 3, sections are taken along various angles through the probe (5), and, the different forms of the sections (9, 9 a), as shown in FIGS. 4 and 5, in particular their asymmetry, half-value width or curvature in the centre, are used to determine the various geometrical-optical aberrations, as described above. 

1. Method for determining geometrical-optical aberrations up to and including 3rd order in particle-optical, probe-forming systems, in particular scanning electron microscopes, comprising an essentially punctiform source, which emits the particles, lenses for influencing the particle beam, an object, which is imaged by the particles, and a detector for registering the particles or imaging the object, the object (3) being imaged by means of a particle beam focussed on the object (3), and the image (6) being recorded, the process being repeated by means of an overfocussed and an overfocussed beam, which produce the images (6 a) (overfocussed) and (6 b) (underfocussed), the images (6, 6 a, 6 b) being transformed in Fourier space, the transformation of the overfocussed image (7 a) being divided by that of the transformed focussed image (7), and the quotient (8) being obtained, and the transformation of the underfocussed image (7 b) being divided by that of the transformed focussed image (7) and the quotient (8 a) being obtained, characterised in that both quotients are reverse transformed and thereby the brightness profiles of the probes (5, 5 a), that is to say of the images of the source in overfocus and underfocus, are determined, the asymmetry (AS) of the profiles (9, 9 a) with respect to the centre, the width (BR) of the profiles (9, 9 a), in particular the half-value width, and/or the curvature (KR) of the profiles (9, 9 a) in the centre are determined, the differences of the profiles (9, 9 a) of the probes (5, 5 a) with respect to these parameters are used to determine the image aberrations.
 2. Method according to claim 1, characterised in that the Fourier transformation and/or the reverse transformation is obtained by mathematical and/or optical means, preferably by generating the diffraction pattern.
 3. Method according to one of the preceding claims, characterised in that the particle beam is influenced with electrical and/or magnetic multipoles.
 4. Method according to one of the preceding claims, characterised in that the width of the defocussed image (5, 5 a) of the source (1) is at least ten times greater than the width of the focussed image of the source (1) or of the source (1) itself.
 5. Method according to one of the preceding claims, characterised in that, sections are taken at angular intervals, in particular every 15 degrees, through the probe profiles in overfocus and underfocus, and the aforementioned parameters are determined for each section.
 6. Method according to claim 5, characterised in that, for determining the image aberration of the 2nd order axial coma, the mean values of the asymmetries (AS) of the sections through the probes in overfocus and underfocus in dependence on the section angles “w” are formed, and the magnitude and orientation of the one-fold components of these mean values are determined, preferably by Fourier analysis with respect to the section angle “w”.
 7. Method according to claim 5, characterised in that, for determining the image aberration of the three-fold 2nd order astigmatism, the mean values of the asymmetries (AS) of the sections through the probes in overfocus and underfocus in dependence on the section angle “w” are formed, and the magnitude and orientation of these mean values are determined, preferably by Fourier analysis over the section angle “w”.
 8. Method according to claim 5, characterised in that, for determining the defocussing, the difference between the widths (BR) of the sections through the probes in overfocus and underfocus in dependence on the section angle “w” is formed, and the magnitude of the zero-fold component of these differences are determined preferably by Fourier analysis over the section angle “w”.
 9. Method according to claim 5, characterised in that, for determining the two-fold 1st order astigmatism, the difference between the widths (BR) of the sections through the probes in overfocus and underfocus in dependence on the section angle “w” is formed, and the magnitude of the two-fold component of this difference is determined, preferably by Fourier analysis over the section angle “w”.
 10. Method according to claim 5, characterised in that, for determining the 3rd order spherical aberration, the difference between the curvature KR of the sections through the probes in overfocus and underfocus is formed in dependence on the section angle “w” and the magnitude of the zero-fold component of these differences is determined, preferably by Fourier analysis over the section angle “w”.
 11. Method according to claim 5, characterised in that, for determining the 3rd order stellar aberration, the difference between the curvature KR of the sections through the probes in overfocus and underfocus is formed in dependence on the section angle “w”, and the magnitude of the two-fold component of these difference is determined, preferably by Fourier analysis over the section angle “w”.
 12. Method according to claim 5, characterised in that, for determining the four-fold 3rd order astigmatism, the difference between the curvature KR of the sections through the probes in overfocus and underfocus in dependence on the section angles “w” is formed, and the magnitude of the two-fold component of these difference is determined, preferably by Fourier analysis over the section angle “w”.
 13. Method according to claim 10, characterised in that, for determining the 3rd order spherical aberration, instead of the difference in curvature (KR), the difference of a linear combination of curvature (KR) and width (BR) is used in the form α*BR+β*KR α and β being determined empirically and representing the respective mean value with respect to the section angle “w”. 